Question

The current price of oil (P) is approximately $50 per barrel, while global oil consumption (Q) is approximately 100 million barrels per day. Suppose the daily demand and supply of oil can be apporximated as linear functions of price, given by:

Demand: Qd = a + bP Supply: Qs = c + dP

where Qd and Qs are quantities demand and supplied per day (measured in millions of barrels) P is price (measured in dollars per barrel); while a, b, c and d are numbers.

A.) Assuming the current price elasticity of daily demand for oil is -0.50 and the current price elasticity of daily supply is 0.50, coupled with the market currently being in equalibrium (i.e., P=50 and Qd = Qs (i.e.,Q) = 100 are the equailibrium price and quantity) determine the values of a, b, c,and d.

B.) Now, suppose world leaders reach an agreement to reduce global carbon emission by imposing a $t per barrel tax on consumers of oil with the goal of reducing global daily oil consumption by 20% determine the value of t sufficient to reach this target reduction in oil consumption.

Answer 1

a) In equilibroum, demand = supply.

Thus, a + bP = c + dP

which gives (a-c) = (d-b)P

Since Q = 100 and P = 50 (given the economy is in equilibrium), we get:

(a-c)/(d-b) = 50 .........(1)

Also, given the elasticity of demand and supply, we get two more equations:

-0.50 = DQ/DP. P/Q

whic gives 0.50 = b. (50/100) = b/2

Thus, b = 1

Similarly for elasticity of supply, we get:

0.50 = d/2, thus d = 1

Putting the values of b and d in the equation (1), we get:

a = c

Thus, Qd = a - P which gives a = c = 50.

B) Given, new Q ´= 80, new price = (50+t)

Thus, new demand curve equation is : Qd = a + b(P+t) which gives:

80 = 50 + (P+t) which gives t = 30.